Question

Three years ago Maria as 7 times older than her sister kate. Two years ago, Maria was 4 times older than Kate. A year ago, Maria was 3 times older than Kate. How old is Maria?

Answer 1

Let's use algebra to solve this problem. Let's say Maria's current age is "M" years and Kate's current age is "K" years.

According to the information given:
1. Three years ago: M - 3 = 7(K - 3)
2. Two years ago: M - 2 = 4(K - 2)
3. A year ago: M - 1 = 3(K - 1)

Now we have a system of three equations. Let's solve for M and K:
Equation 1: M - 3 = 7K - 21
Equation 2: M - 2 = 4K - 8
Equation 3: M - 1 = 3K - 3

Solve Equation 3 for M: M = 3K - 2
Substitute M in Equation 2: 3K - 2 - 2 = 4K - 8
Simplify Equation 2: K = 6

Now that we know Kate's current age (K = 6), we can find Maria's current age using Equation 3: M = 3K - 2 = 3(6) - 2 = 16.

So, Maria is currently 16 years old.